The problem of determining fluid mass in a micro-g space environment is not a new one. During the past 60 years there have been several methods proposed. Considerable development effort has been expended to demonstrate some of these methods. In all cases the methods involve some secondary characteristic property of the system or comparison mass to deduce the unknown mass. Unfortunately, nearly every method requires fluid-specific calibrations as a direct result of relying on secondary physical properties. Some methods lose resolution as the fluid mass approaches depletion, when the residual quantity information is most useful.
The methods that have received the greatest attention in recent years include Pressure-Volume-Temperature (PVT); Propellant Gauging System (PGS); Capacitance Probes; Optical Mass Gauge Sensor (OMGS); and Book-Keeping Method. These can be summarized briefly as follows:
The PVT method determines the ullage volume and by deduction the liquid volume and mass. The method uses a reciprocating mechanical plunger/bellows to pressurize the fluid. Equilibrium thermodynamic relations are used to compute the volume based on system pressure and temperature data. The assumption of ullage temperature uniformity is required for accuracy and this condition is not always achievable in large vessels (e.g., LH2) or near liquid depletion when the ullage is large and the pressure decreases. Non-condensable GHe is also required for cryogenic fluids. Empirical corrections and fluid-specific thermophysical data are also required. An uncertainty of ˜5% may be achievable with some fluids (LO2).
The PGS method uses a heat pulse technique similar to the heat pulse method used for successfully gauging superfluid helium in 1 g. It attempts to determine the thermal capacitance of the residual liquid. However, the low thermal conductivity of classical fluids results in special gauging corrections, and there may be uncertainty in the heater power, fluid temperature uniformity, and the external temperature environment. A mission unique thermal model of the vessel is required in addition to calibration curves.
The capacitance method relies on the dielectric constant properties of the fluid and vapor. A coaxial capacitance probe must always be calibrated for each vessel. It requires that the fluid be settled to define a flat interface and has typically been used in conjunction with low-level thrusting. It may be applicable in zero-g if the vessel internal vane arrangement is designed to achieve the desired interface profile, but this is not a simple matter. Uncertainty may arise from liquid meniscus effects. A similar capacitance geometry has been employed with slush hydrogen measurements.
The OMGS method has been described for solid and liquid hydrogen (LH2). It uses the vessel internal surface as an “integrating sphere” to obtain light transmittance data. Calculation of the attenuation factor leads to the mass determination. This method requires exacting knowledge of the optical absorption characteristics of the fluid, precision laser tuning and bandwidth, thermal regulation of the laser, and special coating of the vessel internal surface. Because every fluid has different attenuation properties, the method must be customized for each fluid.
The book-keeping method is a quasi-direct approach to mass gauging. Simply stated, it tracks the fluid outflow and in principle provides the residual mass if the initial mass value is known. In the case of vented vessels that employ vapor-cooled shields, low pressure loss/high sensitivity volumetric flow-metering requires corrections for pressure and temperature to accurately determine mass flow rate. Fluid specific calibration corrections are also required. For actual fluid transfer uncertainty arises from the possibility of two-phase flow or from over-ranging the flow meter. Uncertainty increases toward fluid depletion due to error accumulation.
Only recently has the resonant frequency approach received much attention. Rudy Werlink at NASA/KSC, in collaboration with Carthage College, has developed a gauging system that uses modal analysis. To our knowledge the project has flown on two missions in 2011 and 2012 on the NASA research aircraft that provides a few minutes of low g experiment time during its parabolic flight trajectories. Flight test data shown in FIG. 6 of reference 6 are much more linear than the lab data presented in that figure. Two important points should be made when comparing that research to the MAGA invention: 1) our design and earliest (unfunded) proposal to NASA pre-dates the KSC project, and 2) the fundamental approach of MAGA differs from that of NASA-KSC in that we are not trying to measure intrinsic oscillations of the stand-alone vessel/fluid proper, but rather as it constitutes a subsystem of the overall vessel-fluid-support structure, as shown in FIG. 1. The NASA/KSC approach is much more complicated and difficult to implement because many intrinsic modes, both mechanical and acoustical, are likely to exist as a function of the fluid distribution. This situation is eliminated when the fluid-containing vessel is coupled to a support structure via struts, rods, tubes, straps or other tension or compression linkages and the resonance data are analyzed as a simple in-situ spring/mass resonant system.
A cantilever spring/mass system for determining an unknown solid or fluid mass has been described by Jun Isobe et al. (Ref. 7). There are several significant differences between that invention and the present invention: 1) it requires a single cantilever and a test mass to determine the spring constant in a one degree of freedom constraint; 2) to measure a fluid mass it requires a bellows and/or bladder to position the fluid; 3) it is primarily used to measure small experimental masses on the ISS; 4) it uses a “pinger” to excite natural resonance, as opposed to the MAGA swept frequency excitation (forced resonance); 5) it does not incorporate resonant amplitude (energy) data as part of the mass determination (see FIG. 3 of this application); 6) it is not applicable to any practical cryogenic fluid vessel which involves an extensive strut or strap support system to reduce parasitic heat leaks.
In summary, most of the foregoing fluid gauging methods have drawbacks that are directly associated with the fact that secondary fluid properties are required to determine mass, and fluid-specific calibrations or modifications are usually required. By contrast MAGA uses the defining property of mass itself to make this determination, viz., the resonant response of the mass in both frequency and amplitude to an applied oscillatory force. The MAGA method is implemented in situ and does not require additional test masses or external measuring apparatus.